Materials that can undergo considerable deformation before failure have been widely used as seismic isolators in bridges, high-rise buildings, nuclear power plants and other critical infrastructure as a passive protection measure against earthquakes. Fundamental research of such materials is extremely important, so it is of great interest to study these materials. The dispersive behavior of time-harmonic waves propagating in pre-stressed compressible and incompressible media is studied. The propagator matrix technique which is very useful for layered media is used to obtain the dispersion relation in explicit form. Two different geometries of pre-stressed composite material are shown in Figs. 1 and 2. For the geometry shown in Fig. 1, symmetric and anti-symmetric waves can be decoupled as it is symmetric about the mid-plane, however, the geometry in Fig. 2 is such that the problem cannot be decoupled into symmetric and anti-symmetric waves.

In addition, wave propagation in a pre-stressed compressible elastic layer with constrained boundaries has also been investigated,
where the dispersion relation can be decoupled into symmetric and anti-symmetric cases (Fig. 3).

Analysis of the dispersion relation at low and high wavenumber limits gives the finite wave speeds at *kh* → 0 and *kh* → ∞ where
*kh* is a non-dimensional wavenumber. At the high wavenumber limit, the phase speeds of the fundamental mode and the higher modes tend
to phase speeds of surface wave, interfacial wave or the limiting phase speed of the composite. The dispersion curve and frequency
spectrum are shown in Fig. 4 for a two-parameter compressible neo-Hookean material for a bi-material laminate.

Fig. 1. Pre-stressed equilibrium configuration of a symmetric layered composite.

Fig. 2. Pre-stressed equilibrium configuration of a bi-material laminate.

Fig. 3. Pre-stressed compressible elastic layer with constrained boundaries.

Fig. 4 (a) Dispersion curve and (b) frequency spectrum, of the fundamental mode and next fifteen modes, ξ02: finite phase speed, ξ*R: surface wave speed, ξI: interfacial wave speed, ξCL: limiting phase speed of the composite.

**Related Journal Papers:**

[1] Leungvichcharoen, S. and Wijeyewickrema, A. C., 2003, "Dispersion effects of extensional waves in pre-stressed imperfectly bonded incompressible elastic layered composites", Wave Motion, Vol. 38, pp. 311-325. IF = 1.505 (2010)

[2] Leungvichcharoen, S. and Wijeyewickrema, A. C., 2004, "Stress concentration factor and scattering cross-section for plane SH-wave scattering by a circular cavity in a pre-stressed elastic medium", Journal of Applied Mechanics, JSCE, Vol. 7, pp. 15-20.

[3] Leungvichcharoen, S., Wijeyewickrema, A. C. and Yamamoto, T., 2004, "Anti-symmetric waves in pre-stressed imperfectly bonded incompressible elastic layered composites", International Journal of Solids and Structures, Vol. 41, pp. 6873-6894.

IF = 1.677 (2010)

[4] Wijeyewickrema, A. C., Ushida, Y. and Kayestha, P., 2008, " Wave propagation in a pre-stressed compressible elastic layer with constrained boundaries", Journal of Mechanics of Materials and Structures, Vol. 3, No. 10, pp. 1963-1976. IF = 0.481 (2010)

[5] Wijeyewickrema, A. C. and Leungvichcharoen, S., 2009, "Wave propagation in pre-stressed imperfectly bonded compressible elastic layered composites", Mechanics of Materials, Vol. 41, pp. 1192-1203. IF = 1.901 (2010)

[6] Kayestha, P., Wijeyewickrema, A. C. and Kishimoto, K., 2010 "Time-harmonic wave propagation in a pre-stressed compressible elastic bi-material laminate", European Journal of Mechanics A/Solids, Vol. 29, pp. 143-151.
IF = 1.414 (2010)

[7] Kayestha, P., Wijeyewickrema, A. C. and Kishimoto, K., 2011 "Wave propagation along a non-principal direction in a compressible pre-stressed elastic layer", International Journal of Solids and Structures, Vol. 48, pp. 2141-2153.
IF = 1.677 (2010)

[8] Kayestha, P., Rodrigues Ferreira, E. and Wijeyewickrema, A. C., 2013, “Finite-amplitude shear horizontal waves propagating in a pre-stressed layer between two half-spaces”, International Journal of Solids and Structures Vol. 50, No. 22-23, pp. 3586-3596.
IF = 1.871 (2013)

(IF – Journal Impact Factor)

**Related Conference Papers:**

[1] Wijeyewickrema, A. C., Yamamoto, T., and Leungvichcharoen, S., 2001, "Flexural Wave Propagation in Incompressible Pre-stressed Imperfectly Bonded Elastic Composites", Proceedings of the 2001 Mechanics & Materials Conference MMC 2001, June 27-29, San Diego, California, pp. 39.

[2] Leungvichcharoen, S. and Wijeyewickrema, A. C., 2001, "Dispersion Curves for Extensional Waves in Pre-stressed Imperfectly Bonded Incompressible Layered Elastic Composites", Proceedings of the Third International Summer Symposium JSCE, August 08, Tokyo, Japan, pp. 73-76.

[3] Yamamoto, T. and Wijeyewickrema, A. C., 2001, "Flexural Wave Propagation in Pre-stressed Imperfectly Bonded Incompressible Layered Elastic Composites", Proceedings of the Third International Summer Symposium JSCE, August 08, Tokyo, Japan, pp. 81-84.

[4] Yamamoto, T. and Wijeyewickrema, A. C., 2001, "Flexural Wave Propagation in Pre-stressed Incompressible Layered Elastic Composites with an Imperfect Interface", Proceedings of the 56th JSCE Annual Meeting, October 2-4, Kumamoto, Japan, CD-ROM Paper No. I-B231, pp. 462-463.

[5] Leungvichcharoen, S. and Wijeyewickrema, A. C., 2002, "Extensional Wave Propagation in Pre-stressed Imperfectly Bonded Incompressible Layered Elastic Composites", Proceedings of the Third Australasian Congress on Applied Mechanics ACAM 2002, February 20-22, Sydney, Australia, pp. 243-248.

[6] Wijeyewickrema, A. C. and Leungvichcharoen, S., 2002, "Dispersive behavior of extensional waves in pre-stressed imperfectly bonded incompressible layered composites", Proceedings of the 15th Engineering Mechanics Division Conference, ASCE, EM2002, June 2-5, New York, CD-ROM Paper No. 194, 8 pages.

[7] Wijeyewickrema A.C., and Leungvichcharoen, S., 2004, "Dispersion and stability analysis of waves in pre - stressed imperfectly bonded layered composites", Proceedings of the 21st International Congress of Theoretical and Applied Mechanics, August 15-21, Warsaw, Poland, pp. 279.

[8] Leungvichcharoen, S. and Wijeyewickrema, A. C., 2004, "Wave propagation in pre-stressed imperfectly bonded compressible elastic layered composites", Symposium on Mechanics and Materials: In Honor of Professor Leon Keer’s 70th Birthday, ASME IMECE2004, Nov.13-19, Anaheim, CA, pp. 135.

[9] Wijeyewickrema, A. C., 2005, "Dispersive behavior of waves in a pre-stressed elastic layer with constrained boundaries", Proceedings of the Third M.I.T. Conference on Computational Fluid and Solid Mechanics, June 14-17, Cambridge, MA, pp. 382.

[10] Wijeyewickrema, A. C. and Ushida, Y., 2005, "Wave propagation in a pre-stressed compressible elastic layer with constrained boundaries", Proceedings of Recent Advances in Nonlinear Mechanics, Aug. 30-Sept. 01, Aberdeen, Scotland, UK, pp. 142.

[11] Wijeyewickrema, A. C. and Ushida, Y., 2005, "Analaysis of wave motion in a pre-stressed compressible elastic layer with constrained boundaries", JTU-TIT China, 1st JTU-TIT Joint Workshop on Innovation of Creative Engineering, September 12-16, 2005, Shanghai/Xi’an, P. R. China, pp. 3.

[12] Wijeyewickrema A.C., and Leungvichcharoen, S., 2008, "Dispersive behavior of waves in pre-stressed imperfectly bonded compressible elastic layered composites", Proceedings of the 22nd International Congress of Theoretical and Applied Mechanics, August 24-29, Adelaide, Australia, pp. 261.

[13] Kayestha, P. and Wijeyewickrema, A. C., 2009, "Dispersive behavior of time-harmonic waves traveling in pre-stressed compressible laminate", Multidisciplinary International Student Workshop 2009, August 4-5, Tokyo Institute of Technology, Japan.

[14] Kayestha, P. and Wijeyewickrema, A. C., 2009, "Dispersion effects of waves in a pre-stressed compressible elastic bi-material laminate", Recent Advances in Nonlinear Mechanics (RANM 2009), August 24-27, Kuala Lumpur, Malaysia, pp. 68-69.

[15] Kayestha, P. and Wijeyewickrema, A. C., 2009, "Wave propagation in a perfectly bonded pre-stressed compressible bi-layered composite", Proceedings of the Eleventh International Summer Symposium JSCE, September 11, Tokyo, Japan, pp. 49-52.

[16] Kayestha, P., Wijeyewickrema, A. C. and Kishimoto, K., 2010 “Dispersion effects of waves propagating along a non-principal direction in a compressible elastic medium”, 9th Taiwan-Japan Student Seminar, July 25-27, Awaji-shima, Kobe, Japan, Paper #5.

[17] Kayestha, P., Wijeyewickrema, A. C. and Kishimoto, K., 2010 “Dispersion effects of waves in a compressible elastic layer propagating along a non-principal direction”, 2nd Multidisciplinary International Student Workshop (2nd MISW), August 5-6, Tokyo Institute of Technology, Japan, pp. 76.